derivative of (xsqrt(2x+1)/(sqrt(4-5x)))

解答

\frac{d}{d x} (\frac{x 2 x + 1}{4 - 5 x})

\frac{- 20 x ^{2} + 19 x + 8}{2 ( 4 - 5 x ) 2 x + 1 - 5 x + 4}

求解步骤

\frac{d}{d x} (\frac{x 2 x + 1}{4 - 5 x})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x 2 x + 1 ) 4 - 5 x - \frac{d}{d x} ( 4 - 5 x ) x 2 x + 1}{( 4 - 5 x ) ^{2}}

\frac{d}{d x} (x 2 x + 1) = \frac{3 x + 1}{2 x + 1}

\frac{d}{d x} (4 - 5 x) = - \frac{5}{2 4 - 5 x}

= \frac{\frac{3 x + 1}{2 x + 1} 4 - 5 x - ( - \frac{5}{2 4 - 5 x} ) x 2 x + 1}{( 4 - 5 x ) ^{2}}

化简

\frac{\frac{3 x + 1}{2 x + 1} 4 - 5 x - ( - \frac{5}{2 4 - 5 x} ) x 2 x + 1}{( 4 - 5 x ) ^{2}} : \frac{- 20 x ^{2} + 19 x + 8}{2 ( 4 - 5 x ) 2 x + 1 - 5 x + 4}

= \frac{- 20 x ^{2} + 19 x + 8}{2 ( 4 - 5 x ) 2 x + 1 - 5 x + 4}

\int \frac{4 - 3 x ^{2}}{( 3 x ^{2} + 4 ) ^{2}} d x

\int q^{2} cos (4 q) d q

t an g e n t 3 x^{2} + 3 x - 5

\frac{\partial}{\partial x} (\frac{2 x}{y})

d er i v a t i v e y = x^{4} e^{3 x}